HIERARCHICAL AND MIXING PROPERTIES OF STATIC COMPLEX NETWORKS EMERGING FROM FLUCTUATING CLASSICAL RANDOM GRAPHS

Sumiyoshi Abe () and Stefan Thurner
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Sumiyoshi Abe: Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan

International Journal of Modern Physics C (IJMPC), 2006, vol. 17, issue 09, 1303-1311

Abstract: The Erdös–Rényi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

Keywords: Static complex network; fluctuating random graph; hierarchial property; mixing; 89.75.Hc; 89.75.-k; 05.70.Ln (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0129183106009837

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